1 2 In y = 1 In x +In(x + 1) + In C 3

Q: 4 For which values of a e R is the function f(x + iy) = (a²x – axy)+ i ax? + ay an entire function?

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Q: For which values of x is f ' (x) < 0?

A: Given,

Q: Find y as a function of a if y" – 8y" + 15y/ = 8e", y(0) = 28, y(0) = 14, y"(0) = 12. y(x) =…

A: We have to find the solution of differential equation.

Q: Evaluate the function at the given values of the independent variables. z = x? + 3xy + y; x = 1, y =…

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Q: A function of the form y ax + bx + c, a + 0, is called a/an function.

A: The given function is, y=ax2+bx+c, a≠0 For the given function, the degree of the function is 2.

Q: For what value of x does the function g(x) x - 2x concave downward? В. A. x -1 D. x< 2 C. x -2 1/3

A: The graph of y = g (x) is concave downward on those intervals where y = g "(x) &lt; 0.

Q: Use a formula to express w as a function of t if w = s3 + 4 and s = 2t – 5.     b.If f(x) = x3 and…

A: Apply the formula a-b3=a3-b3-3aba-b and then simplify.

Q: Suppose z is implicitly defined as a function of x, y, by means of the equation 2* + 6z?y = 2y – 3x?…

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Q: Find the value of the constant k that makes the function continuous.

A: We shall try and understand this concept, in simple terms.A function is continuous at a point, if…

Q: Evaluate y' of the given functions: xy² = x²

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Q: Eliminate the arbitrary constant on the given function : 2x y = cje + Cze %3D

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Q: 5. Which of the following equivalent forms of the function f(x) = 4x² + 4x – 24 is the most suitable…

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Q: 01: If the function w = f(x, y) and x = 2u + 3v, y = 3u – 2v, Find Wuy ?

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Determine the values of C for which the function below is continued at the point x=2. Cx²+2x, if x <…

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Q: Which of the following relations from R to R is a function? a) f (x) = 1/x b) f (x) = (x) 1/2 c) f…

A: Given relations are  a fx=1xb fx=xc fx=x2

Q: a) Find the local extreme values of the function f(x,y) = 2xy – x² – 2y2 +3x + 4. %3D

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Q: -2 I= 3 T = 1 f (x)= 2 2-4 otherwise (z+2)(r-3)

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Q: (c) Find the largest and the smallest values of the function f(x) = re2 on the interval –1 <r<1.

A: We will solve the following.

Q: Consider the function f(x) = 4sin(π/2 x) + 2  Find the first three positive values of x for which…

A:

Q: Express the function ℎ(?)=1?+1h(x)=1x+1 in the form ?∘?f∘g. If ?(?)=?+1g(x)=x+1, find the function…

A: Consider the given functions h(?) and h(x)

Q: Use a formula to express w as a function of t if

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Q: Express y as a function of x. The constant C is a positive number.  In(y-1)=-5x+ In C

A: Apply log properties Ln(Y-1)-lnc=-5x ln((y-1)/c)=-5x

Q: is a function of the form f(x) = Ca", where a > 0, a + 1, and C +0 are real and C is the A(n)…

A: A(n) ______ is a function of the form f(x) = Cax, where a &gt; 0, a # 1, and C≠0 are real numbers.…

Q: Find all values of x for which f(x) satisfies the indicated conditions. f(x) = x? – 5x, f (x) < 0

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Q: . Determine if y is a function of x in x = y? + 5.

A: Given equation - x = y2+5Let's solve for y =- y2 = x-5y = x-5       ........(1)

Q: Find f'(x) and find the value(s) of x where f'(x) = 0. f(x) = f'(x) = X x² +49

A: We need to find x values where f'(x)=0

Q: Any function of the form f(x, y) = ax*y" where a is a real number and k, n are positive integers…

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Q: 19ver. Find y as a function of x if a?y" – 7xy' + 16y = 0, %3D y(1) = –5, y'(1) = –4. y =…

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Q: 11. Let f be the function f(x) = x² In x. For what value of x is the slope of the line tangent to…

A: Consider the given function fx=x2lnx

Q: Find the first 3 iterates of the function f (x) = 3x when xo = 2? D 5, 6, 54 D 5, 15, 45 D 2, 6, 18…

A: To find The first 3 iterates of the function f(x)=3x at x0=2.

Q: Evaluate the function at the given values of the independent variables. = x³ + 3xy + y²; x = -1, y =…

A: z=x3+3xy+y2x=-1  and y=1 Replace the x  and y values in the given function

Q: Evaluate the given function y = x² + C,x + C,e¬* is equal to А. ху' — х?у — у" (х — 1) B.xy' = x² +y…

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Q: Find and simplify the function h(x, y, z) = xy at the given value (4, 6, 31). 12 17 12 31 24 31 4 31…

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Q: 7. Which function(s) have/has a zero at x = 2? y = 2* +2 b. y = x² +2 c. y = |x +2| d. y = Vx - 2 a.

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Q: Which of the following functions is not differentiable in C? (A) f (z)=e (C) both (A) and (B) (B) f…

A: We have to choose correct one

Q: 4. Use e – d definition and show that the function 4.x? – y? - if (x, y) # (1, –2) 2x + Y f (x, y) =…

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Q: Use a formula to express w as a function of t if w = s2 + 1 and s = t − 2. w =

A: Explanation of the answer is as follows

Q: b. z = x² + 12xy + 2y², if 4x² + y² = 25. %3D

A:

Q: Use a formula to express w as a function of t if w = s +1 and s =t- 6.

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Q: If f(z) = u + iv is analytic function of z, show that a2 a2 2C. ây? 7 Ju? = p(p-1)uP-?|f'(2)}?

A:

Q: 2x he function f (x,y) = is said to be homogenous to what degree? A) zero B) one c) non-homogenous…

A: Topic:- calculus

Q: Express the statement as a formula that involves the given variables and a constant of…

A: Given: y is directly proportional to the square of x And inversely-proportional to the cube of z x=5…

Q: the domain of the function : y = In(x² + x + 1) is [0,0) Select one: O True O False

A: From the given problem:   y=lnx2+x+1   We know that logax is defined when x,a&gt;0.

Q: If f(x.y,z) In(xz) – 2xy2z, find fzxy at the point (0.5, 1,-1) a) b) - 1 c) 8 d) - 2 e) - 4 g) None…

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Q: 5. Which of the following functions f(x, y) are homothetic? 2(xy)? (b) (xy)? +1 (a) (xy)? +1 (c) x²…

A: (a) The given function is: fx,y=xy2+1

Q: 11. Let f be the function f (x) = x² In x. For what value of x is the slope of the line tangent to…

A:

Q: Find the lengths of the functions of y over the given interval. y² + 1)*¨ from y = 1 to y = 3 61/3…

A: Here we need to find the length of curve

Q: 7. Which function(s) have/has a zero at x = -5? a. y = 2*+5-1 b. y = x² -5 C. y = |x - 5| d. y %3 (x…

A: We have to find the function

Q: Consider the function k(x)=ax−12, where a is a constant. Given k(2)=24, calculate a.

A: Concept- Substitute the value of x in given function K(x).

Q: 14 Which function is linear? Select all that apply. A y 6x+8 4x+ 2 3 Cy = x + 1 Dy = 2x + 8

A: We have to find the linear function